A vane pump typically includes a cylindrical rotor rotatable inside of an oval-shaped rotor chamber defined by a cam ring around the rotor. The cam ring and the rotor define a crescent-shaped cavity therebetween which is divided into a plurality of pump chambers by a corresponding plurality of flat vanes in radial vane slots in the rotor. The pump chambers expand in an inlet sector of the crescent-shaped cavity and collapse in a discharge sector of the crescent-shaped cavity as the rotor rotates. A thrust plate and a pressure plate on opposite sides of the cam ring cover the rotor chamber and are squeezed together by a plurality of hold-down springs or the like. Fluid in a discharge chamber of the vane pump at a discharge pressure thereof reacts against the pressure plate to further clamp the cam ring between the pressure plate and the thrust plate. A significant fluid pressure differential across the pressure plate within an area defined by the silhouette of the rotor chamber induces flexure of the pressure plate into the rotor chamber. A clearance dimension between the thrust plate, the pressure plate and the rotor calculated to accommodate such flexure exceeds a corresponding clearance dimension calculated only to minimize friction between the thrust plate, the pressure plate and the rotor. Fluid leakage from the pump chambers attributable to the extra clearance for flexure of the pressure plate reduces the volumetric efficiency of the vane pump.